Question: If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f(t) and cumulative distribution function

If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f(t) and cumulative distribution function F(t), then the hazard function is defined to be the function h(t) = f(t)

1 − F(t)

The hazard function is the rate of failure per unit time, expressed as a proportion of the items that have not failed.

a. If T ∼ Weibull(????, ????), find h(t).

b. For what values of ???? is the hazard rate increasing with time? For what values of ???? is it decreasing?

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